Thanks for all the replies and the reassurance - I mainly wanted to get my expectations in check! It's good to know this is the norm.

One thing to note though is that during the meetings, they mention that they will email me certain pieces of information - this is partially why I email immediately after the meetings. I could understand if they get busy and forget... but is it unreasonable for me to send follow up emails inquiring about things that they had said they would email to me?

I contacted a professor at the local university (I live near a top uni in Canada) who happens to study something that I would be interested in studying and they were very receptive to taking me on as a student!

However, we have been exchanging emails and I'm getting worried. They replied very quickly to my first emails, but said they were in a conference out of town so we didn't meet in person until around a month after our initial correspondence. Then after we met up, I sent an email the next day following up on some things we talked about during our meeting and they didn't reply for another month... I sent maybe 5 follow up emails spread out across a few days or weeks to try and get in contact with them. Finally, they responded saying they were busy teaching a class - which I completely understand, professors being busy with their teaching and research and considering I'm not even their official student. We set up another time to meet up in person, and during the meeting we set some goals before the application deadline. They said they would supervise me to write 2 separate pieces in preparation for my Masters / PhD. I sent another email the next day following up on that meeting and outlining the two pieces. This was a month ago, and despite a couple follow up emails, I haven't heard back.

Whenever we meet up in person, they are very receptive and helpful. But once I leave their office, it feels like I can't connect with them at all. I'm worried that if I do begin a PhD with this professor that these communication difficulties may remain... Am I overthinking this? I know that professors get busy, and considering I'm not officially a student yet, this professor doesn't "owe" me anything. I have been working for the past 3 years and I'm used to a work environment with a lot of communication. Are my expectations inaccurate for the postgrad world?